The total number of matrices

Question:

The total number of matrices

$A=\left(\begin{array}{ccc}0 & 2 y & 1 \\ 2 x & y & -1 \\ 2 x & -y & 1\end{array}\right),(x, y \in R, x \neq y)$ for which

$\mathrm{A}^{\mathrm{T}} \mathrm{A}=3 \mathrm{I}_{3}$ is :-

 

 

  1. 6

  2. 2

  3. 3

  4. 4


Correct Option: , 4

Solution:

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